Artículo
Conditional stability and convergence of a fully discrete scheme for three-dimensional Navier–Stokes equations with mass diffusion
Autor/es | Guillén González, Francisco Manuel
Gutiérrez Santacreu, Juan Vicente |
Departamento | Universidad de Sevilla. Departamento de Ecuaciones Diferenciales y Análisis Numérico |
Fecha de publicación | 2008 |
Fecha de depósito | 2016-05-16 |
Publicado en |
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Resumen | We construct a fully discrete numerical scheme for three-dimensional incompressible fluids with mass diffusion (in density-velocity-pressure formulation), also called the Kazhikhov–Smagulov model. We will prove conditional ... We construct a fully discrete numerical scheme for three-dimensional incompressible fluids with mass diffusion (in density-velocity-pressure formulation), also called the Kazhikhov–Smagulov model. We will prove conditional stability and convergence, by using at most C0-finite elements, although the density of the limit problem will have H2-regularity. The key idea of our argument is first to obtain pointwise estimates for the discrete density by imposing the constraint lim(h,k)→0 h/k = 0 on the time and space parameters (k, h). Afterwards, under the same constraint on the parameters, strong estimates for the discrete density in l ∞(H1) and for the discrete Laplacian of the density in l 2(L2) are obtained. From here, the compactness and convergence of the scheme can be concluded with similar arguments as we used in [Math. Comp., to appear], where a different scheme is studied for two-dimensional domains which is unconditionally stable and convergent. Moreover, we study the asymptotic behavior of the numerical scheme as the diffusion parameter λ goes to zero, obtaining convergence as (k, h, λ) → 0 towards a weak solution of the density-dependent Navier–Stokes system provided that the constraint lim(λ,h,k)→0 h/(λ2k) = 0 on (h, k, λ) is satisfied. |
Agencias financiadoras | Ministerio de Educación y Ciencia (MEC). España |
Identificador del proyecto | BFM2003–06446-C02-01 |
Cita | Guillén González, F.M. y Gutiérrez Santacreu, J.V. (2008). Conditional stability and convergence of a fully discrete scheme for three-dimensional Navier–Stokes equations with mass diffusion. SIAM Journal on Mathematical Analysis, 46 (5), 2276-2308. |
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